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3 years ago

Colin knows 10 Vocabulary terms. Everyday he wants to learn three new Words. explain the y-intercept in context to the scenario

Mathematics

1 answer:

ANTONII [103]3 years ago

8 0

Before he started he knew 10 vocabulary items. Hence, the y-intercept is (0, 10), 0 being the 0th day.

He learns 3 new words every day, so the slope is 3.

The equation is y = 3x + 10.

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2. Solve the system of equations. Write your answer in parametric vector notation. X, +5x2 + 4x3 + 3x4 +9xs = 18 2x, +6x2 + 4x3

ratelena [41]

Answer:

The system is inconsistent.

Step-by-step explanation:

The system is

$x_1+5x_2+4x_3+3x_4+9x_5=18\\2x_1+6x_2+4x_3+6x_4+6x_5=28\\3x_1+7x_2+4x_3+10x_4+x_5=41\\4x_1+6x_2+2x_3+7x_4+4x_5=29$

The associated matrix to the system is

$\left[\begin{array}{cccccc}1&5&4&3&9&18\\2&6&4&6&6&28\\3&7&4&10&1&41\\4&6&2&7&4&29\end{array}\right]$

Now we use row operations to find the echelon form of the matrix:

1. We substract to row 2, two times the row 1.

We substract to row 3, three times the row 1.

We substract to row 4, four times the row 1 and obtain the matrix

$\left[\begin{array}{cccccc}1&5&4&3&9&18\\0&-4&-4&0&-12&-8\\0&-8&-8&1&-26&-13\\0&-14&-14&-5&-32&-43\end{array}\right]$

2. We multiply the second row of the preview step by -1/4. We obtain the matrix

$\left[\begin{array}{cccccc}1&5&4&3&9&18\\0&1&1&0&3&2\\0&-8&-8&1&-26&-13\\0&-14&-14&-5&-32&-43\end{array}\right]$

We add to row 3, eight times the row 2.

We add to row 4, fourtheen times the row 2 and obtain the matrix

$\left[\begin{array}{cccccc}1&5&4&3&9&18\\0&1&1&0&3&2\\0&0&0&1&-2&3\\0&0&0&-5&10&-155\end{array}\right]$

4. We add to row 4 of the preview step, five times the row 3 and obtain the matrix

$\left[\begin{array}{cccccc}1&5&4&3&9&18\\0&1&1&0&3&2\\0&0&0&1&-2&3\\0&0&0&0&0&-140\end{array}\right]$

Using backward substitution we have that

$0x_5=-140$ , then $0=-140$ and this is absurd. Then The system is inconsistent.

4 0

3 years ago

How many 1/4 cup servings are in 3 cups of pasta?

4vir4ik [10]

Answer:

Explanation:

1/4 × 12 = 3

5 0

3 years ago

Read 2 more answers

Solve : 20-9x=11 4(2x+1)=8 5(2x+5)=-15 3(8x+1)=-21

laila [671]

20-9x=11
-9x=11-20
-9x= -9
x= -9/(-9)
x=1

4(2x+1)=8
2x+1=8/4
2x+1=2
2x=2-1
2x=1
x=1/2
x=0.5

5(2x+5)=-15
2x+5= -15/5
2x+5= -3
2x= -3-5
2x= -8
x= -8/2
x=-4

3(8x+1)=-21
8x+1= -21/3
8x+1= -7
8x= -7-1
8x =-8
x= -8/8
x= -1

4 0

3 years ago

If a and b are real numbers and if y = ax + b is a direct variation equation, what do you know about a and b?

Alenkasestr [34]

y = ax + b
We observe that the given equation is the generic equation of a line.
Where,
a = represents the slope of the line. That is, the rate of change of the given function. (in this case it is constant).
b = is the cut point with the y axis.

8 0

3 years ago

4 – 15 ÷ (30 – 33) =

cupoosta [38]

Answer: 9

Step-by-step explanation:

We will use the Order of Operations to solve.

Given:

4 – 15 ÷ (30 – 33)

Subtract 33 from 30:

4 – 15 ÷ (– 3)

Divide -15 by -3:

4 + 5

Add 4 to 5:

7 0

2 years ago

Read 2 more answers